However,
this does not necessarily extend to a symmetry at the quantum
level. To define the quantum gauge theory, we note that the tangent
space at any point \((P,A)\in \mathsf {Bun}_G^\nabla (\Sigma )\)  can be identified with
\(\Omega ^1(\Sigma ;\operatorname{Ad}(P))\) , and thus an
\(\mathsf {Aut}(P)\) -invariant symplectic form on \(\mathsf {Bun}_G^\nabla (\Sigma )\)  can be
defined by [1]}
\(\omega (A_1,A_2)=\frac{1}{4\pi ^2}\, \int _\Sigma \, \text{Tr}_{\mathfrak {g}}\big (A_1\wedge A_2\big ) \ ,\) 
